26 research outputs found
On products of skew rotations
Let , be two time-independent Hamiltonians with one
degree of freedom and , be the one-parametric groups of
shifts along the orbits of Hamiltonian systems generated by , . In
some problems of population genetics there appear the transformations of the
plane having the form under some
conditions on , . We study in this paper asymptotical properties of
trajectories of .Comment: 13 pages, 10 figure
Non-Equilibrium Statistical Physics of Currents in Queuing Networks
We consider a stable open queuing network as a steady non-equilibrium system
of interacting particles. The network is completely specified by its underlying
graphical structure, type of interaction at each node, and the Markovian
transition rates between nodes. For such systems, we ask the question ``What is
the most likely way for large currents to accumulate over time in a network
?'', where time is large compared to the system correlation time scale. We
identify two interesting regimes. In the first regime, in which the
accumulation of currents over time exceeds the expected value by a small to
moderate amount (moderate large deviation), we find that the large-deviation
distribution of currents is universal (independent of the interaction details),
and there is no long-time and averaged over time accumulation of particles
(condensation) at any nodes. In the second regime, in which the accumulation of
currents over time exceeds the expected value by a large amount (severe large
deviation), we find that the large-deviation current distribution is sensitive
to interaction details, and there is a long-time accumulation of particles
(condensation) at some nodes. The transition between the two regimes can be
described as a dynamical second order phase transition. We illustrate these
ideas using the simple, yet non-trivial, example of a single node with
feedback.Comment: 26 pages, 5 figure
Observation of Precipitation Evolution in Fe-Ni-Mn-Ti-Al Maraging Steel by Atom Probe Tomography
We describe the full decomposition sequence in an Fe-Ni-Mn-Ti-Al maraging steel during isothermal annealing at 550 °C. Following significant pre-precipitation clustering reactions within the supersaturated martensitic solid solution, (Ni,Fe)3Ti and (Ni,Fe)3(Al,Mn) precipitates eventually form after isothermal aging for ~60 seconds. The morphology of the (Ni,Fe)3Ti particles changes gradually during aging from predominantly plate-like to rod-like, and, importantly, Mn and Al were observed to segregate to these precipitate/matrix interfaces. The (Ni,Fe)3(Al,Mn) precipitates occurred at two main locations: uniformly within the matrix and at the periphery of the (Ni,Fe)3Ti particles. We relate this latter mode of precipitation to the Mn-Al segregation
The Potts model built on sand
We consider the q=4 Potts model on the square lattice with an additional
hard-core nonlocal interaction. That interaction arises from the choice of the
reference measure taken to be the uniform measure on the recurrent
configurations for the abelian sandpile model. In that reference measure some
correlation functions have a power-law decay. We investigate the
low-temperature phase diagram and we prove the existence of a single stable
phase with exponential decay of correlations. For all boundary conditions the
density of 4 in the infinite volume limit goes to one as the temperature tends
to zero